{"type":"ScholarlyArticle","title":"Fixing Tournaments for Kings, Chokers, and More","authors":[{"name":"Michael P. Kim","slug":"michael-p-kim","given":"Michael P.","family":"Kim","affiliation":""},{"name":"Virginia Vassilevska Williams","slug":"virginia-vassilevska-williams","given":"Virginia Vassilevska","family":"Williams","affiliation":""}],"abstract":"We study the tournament fixing problem (TFP), which asks whether a tournament organizer can rig a single-elimination (SE) tournament such that their favorite player wins, simply by adjusting the initial seeding. Prior results give two perspectives of TFP: on the one hand, deciding whether an arbitrary player can win any SE tournament is known to be NP-complete; on the other hand, there are a number of known conditions, under which a player is guaranteed to win some SE tournament. We extend and connect both these lines of work. We show that for a number of structured variants of the problem, where our player is seemingly strong, deciding whether the player can win any tournament is still NP-complete. Dual to this hardness result, we characterize a new set of sufficient conditions for a player to win a tournament. Further, we give an improved exact algorithm for deciding whether a player can win a tournament.","doi":null,"url":"https://ijcai.org/proceedings/2015/85","pdf":"https://ijcai.org/proceedings/2015/0085.pdf","markdown":"https://ijcai.org/proceedings/2015/85.md","bibtex":"https://ijcai.org/proceedings/2015/bibtex/85","volume":{"slug":"2015","title":"Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2015","url":"https://ijcai.org/proceedings/2015/","year":2015,"location":"Buenos Aires, Argentina","dates":"25–31 July 2015","editors":"Qiang Yang and Michael Wooldridge","isbn":"978-1-57735-738-4","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":"Game Theory","track":"Main Track","number":85,"pages":{"first":561,"last":566},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}